How can I identify the three isomers of dimethylbenzene from a carbon NMR over an H NMR

The actual question is stated as such:
The three isomers of dimethylbenzene are very difficult to identify using H NMR, but instantly identifiable using C NMR. Explain how?

When atoms are experiencing the same chemical environment, their shifts are identical. For each isomer a different number of signals would be observed because of differing symmetry:

1,2-Dimethybenzene = 4 carbon signals
1,3-dimethylbenzene = 5 carbon signals
1,4-dimethylbenzene = 3 carbon signals

I drew you a diagram to help.